Descartes' Rule of Signs for Polynomial Systems supported on Circuits
Algebraic Geometry
2016-08-31 v2 Symbolic Computation
Abstract
We give a multivariate version of Descartes' rule of signs to bound the number of positive real roots of a system of polynomial equations in n variables with n+2 monomials, in terms of the sign variation of a sequence associated both to the exponent vectors and the given coefficients. We show that our bound is sharp and is related to the signature of the circuit.
Keywords
Cite
@article{arxiv.1601.05826,
title = {Descartes' Rule of Signs for Polynomial Systems supported on Circuits},
author = {Frédéric Bihan and Alicia Dickenstein},
journal= {arXiv preprint arXiv:1601.05826},
year = {2016}
}
Comments
25 pages, 3 figures